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FunctionAdvisor/relate - relate the two given mathematical functions
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Calling Sequence
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FunctionAdvisor(relate, math_function_1, math_function_2)
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Parameters
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relate
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literal name; 'relate'
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math_function_1
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Maple name of first mathematical function
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math_function_2
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Maple name of second mathematical function
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Description
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The FunctionAdvisor(relate, math_function_1, math_function_2) command attempts to relate the functions using the internal Maple algorithms. For more information, see convert[to_special_function].
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By default, the output has the simpler or more standard function on the left-hand side. This topic is similar to FunctionAdvisor/specialize, which allows you to specify which function is expressed in terms of the other one. This typically requires additional constraints in the function parameter(s) domain(s).
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Examples
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| (2) |
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| (3) |
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| (4) |
Notice that a relation between KummerU and HermiteH does not exist for arbitrary values of their parameters.
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* Partial match of Hermite against topic HermiteH.
Unable to establish a relation between KummerU and HermiteH
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However, that relation does exist for a specialization of the function parameters
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![[KummerU(a, b, z) = HermiteH(-2*a, z^(1/2))*2^(2*a), And(b = 1/2)], [KummerU(a, b, z) = (1/2)*HermiteH(-2*a+1, z^(1/2))*2^(2*a)/z^(1/2), And(b = 3/2)]](/support/helpjp/helpview.aspx?si=7556/file01733/math124.png)
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and also the converse.
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![ex1 := [HermiteH(a, z) = 2^a*KummerU(-(1/2)*a, 1/2, z^2), And(0 < Re(z)) or And(Re(z) = 0, 0 < Im(z))]](/support/helpjp/helpview.aspx?si=7556/file01733/math133.png)
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The variables used by the FunctionAdvisor command to create the function calling sequences are local variables. Therefore, the previous example does not depend on z.
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![depends([ex1], a), depends([ex1], b), depends([ex1], z)](/support/helpjp/helpview.aspx?si=7556/file01733/math146.png)
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To make the FunctionAdvisor command return results using global variables, pass the function call itself.
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![ex2 := [HermiteH(a, z) = 2^a*KummerU(-(1/2)*a, 1/2, z^2), And(0 < Re(z)) or And(Re(z) = 0, 0 < Im(z))]](/support/helpjp/helpview.aspx?si=7556/file01733/math160.png)
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![depends([ex2], a), depends([ex2], b), depends([ex2], z)](/support/helpjp/helpview.aspx?si=7556/file01733/math164.png)
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| (9) |
You can view the default hierarchy used when calling the FunctionAdvisor command with the keyword relate as first argument using the following
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![`convert/to_special_function/hierarchy`["function"]](/support/helpjp/helpview.aspx?si=7556/file01733/math177.png)
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where functions to the left are selected before functions to the right when constructing the left-hand side of the output.
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